Residue codes are arithmetic error detection codes, e.g., a code preserved under a set of arithmetic operations by a computing system. Use of residue codes enables the detection of errors that may occur in the computing system during the execution of an arithmetic operation with a relatively low overhead use of resources. In order to parallelize processor code, the usage of a single instruction over multiple data (SIMD) has been integrated into various modern processor architectures, e.g., Multimedia Extensions (MMX™), Streaming SIMD Extensions (SSE), and Advanced Vector Extensions (AVX), which are by Intel® of Santa Clara, Calif. The execution circuits that execute these SIMD instructions are vulnerable to software error rate (SER) due to radiation, hard errors due to aging of electromigration, and errors due low voltage operation, among others. Detection of such errors allows proper and safe execution in multiple domains such as in high reliability servers, industrial applications, and functional safety, e.g., autonomous driving. Traditional residue error checking can detect such errors but requires storing a residue code per data element of a SIMD packed vector that undergoes arithmetic processing.